Fast Implementation of DeLong's Algorithm for Comparing the Areas Under Correlated Receiver Operating Characteristic Curves
Fast Implementation of DeLong's Algorithm for Comparing the Areas Under Correlated Receiver Operating Characteristic Curves
复制标题
快速实现 DeLong 算法来比较相关接收器工作特性曲线下的面积
DOI：
10.1109/lsp.2014.2337313
复制
发表时间：
2014-11-01
影响因子：
3.9
通讯作者：
Xu, Weichao
中科院分区：
文献类型：
--
作者：
Sun, Xu;Xu, Weichao
在比较两条或两条以上相关的受试者工作特征曲线下面积的算法中，DeLong算法由于其在实践中实现简单，可能是应用最广泛的算法。但遗憾的是，DeLong算法的时间复杂度为二次阶（样本量的乘积），在样本量较大时耗时且不实用。基于Heaviside函数与样本中阶之间的等价关系，我们改进了DeLong算法，将时间复杂度从二次阶降低到线性阶（样本大小与其对数的乘积）。蒙特卡罗模拟验证了我们在这项工作中的算法发现的计算效率。
Among algorithms for comparing the areas under two or more correlated receiver operating characteristic (ROC) curves, DeLong's algorithm is perhaps the most widely used one due to its simplicity of implementation in practice. Unfortunately, however, the time complexity of DeLong's algorithm is of quadratic order (the product of sample sizes), thus making it time-consuming and impractical when the sample sizes are large. Based on an equivalent relationship between the Heaviside function and mid-ranks of samples, we improve DeLong's algorithm by reducing the order of time complexity from quadratic down to linearithmic (the product of sample size and its logarithm). Monte Carlo simulations verify the computational efficiency of our algorithmic findings in this work.